Question

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 10.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.) (a) the response time is between 7 and 12 minutes (b) the response time is less than 7 minutes (c) the response time is more than 12 minutes

Answer 1

Given that, mean = 10.4 minutes

standard deviation = 1.7 minutes

We want to find, the following probabilities,

a) P(7 < X < 12)

Therefore, required probability is 0.8036

b) P(X < 7)

Therefore, required probability is 0.0228

c) P(X > 12)

Therefore, required probability is 0.1736